(i) , (ii) , (iii)

Let unknown polynomial be . Let and be the quotient and remainder, respectively, when it is divided by . Then,

Then, we have

Given that and . Hence,

and

and

(i)

Given that roots are real and distinct. Therefore,

which is true for all real .
(ii)

Now, and equation has no distinct real roots or equation has real and equal or imaginary roots. Then,

Hence, the least value of is .
(iii)

Now, is real, then

──────────────────────────────────────────────────────────────────────────────────────────